More children are being rushed to the hospital because they were able to push down and twist the cap on a medication bottle and were poisoned by a common drug. A recent research study suggested that...

More children are being rushed to the hospital because they were able to push down and twist the cap on a medication bottle and were poisoned by a common drug. A recent research study suggested that 25% of all preschool children can open a medication bottle and 10 preschool children are selected at random. Let the random variable X be the number of children who can open the bottle.

A company has developed a very inexpensive explosive-detection machine for use at airports. However, if an explosive is actually in a suitcase, the probability of it being detected by this machine is only 0.60. Therefore, several of these machines will be used simultaneously to screen each piece of luggage independently. Suppose a piece of luggage actually contains an explosive.

a. If three machines screen this luggage, what is the probability that exactly one will detect the explosive? What is the probability that none of the three will detect the explosive?

b. If four machines screen this luggage, what is the probability that at least one device will detect the explosive?

c. If five machines screen this luggage, what is the probability that at least one device will detect the explosive?

 d. How many machines are necessary for screening in order to be certain that at least one device will detect the explosive with probability 0.999 or greater?